Slide rule



Oct- 2, 1951 D. L. COLE SLIDE RULE Filedqan. 3o, 194e rc Nw m we N TL ND El. WM u .Q IO NN E e D we m. NN QJ Q Q H Q S s w 3 z 5552 $25k ma DOOOQnhWfuOO COQ 00a` OCW @www OO? OO DON 2 Y E .E w B ou. om om om QN 2|/ o00 Q9/ S zwzw 4 :known horizontal range ofthetarget.

Patented Oct. 2, 1951 SLIDE RULE Donald L. Cole, Groton, Conn.

Application January 30, 1948, Serial No. 5,474

(Granted under the act f March 3,1883, as amended anni so, 192s; 37o 0.o. 757) 3 Claims.

The present invention concerns a device for computing the range of va target relative to an observer and particularly concerns a slide rule -for computing the horizontal range of a marine target relative to a marine observer from observed sound echo'data.

yIn marine operations it is necessary vto make y f determinations of the position of a target relaltive to an observer from under water observations. One system for making such determinations, known as echo ranging, embodies projection from the observer toward the target of a Isound beam, which is reflected by the target jback to the observer. Velapsed time between projection of the sound and return thereof-after reflection; the angle of Data observed include elevation or depression made by the sound path with a horizontal plane of reference at the point of observation; and the azimuth of the target.

Thus, in so-called anti-submarine warfare, it is customary for an observing surface ship to project a sound beam toward a submerged target and to measure the elapsed echo time, angle of depression, and azimuth. In another type of warfare, it is customary for an observing. subtmarine to project a sound beam toward a surface target and to `measu-reathe elapsed .echo time, angle'of elevation, and azimuth byr aprocedure known as-vertical .triangulation listening ranging.

From the/observed dataiin sound echo ranging` of this type it .is possible .toV compute the un- This is accomplished by means.fofwtriangulation. To illustrate, the case of a submarine making` observatons onfa'surface target vessel is considered. In FigureB,`

eR=horizontal range in yardsv (unknown,` tobe computed) r(i-:Angle of elevationiobserved) of soundbeam pathvrelative to horizontalplane at submarine.

Solution of the problem for the unknown values R and S is readily accomplished if it is assumed .that the sound beam follows a straightpath between A `and C along line S and that the sound travels at constant velocity. 'From these assumptions,

S elapsed time `(observed) 2 Xspeed of sound Also the unknownhorizontal range 'Ris computed .from the observed submarine depth D. and the observed angle of elevation 6:V

D(feet) l 3 tan 0 Under actual operating conditions the assumption that the sound beam path lies along a straight line is usually not warranted and under most conditions refraction of the sound beam in the water occurs as indicated in dotted lines in the diagram. Typically, the water body occurs in substantially horizontal layers of different sound-'transmitting characteristics so that a sound beam passing through the layers is refracted in passage from one layer to another. As a result of such refraction, value of the horizontal range R computed in the manner above indicated is not correct and it is necessary to modify the computation to take into account the change in angle 0 and range that occurs with refraction, j

It has been found that the change in angle 0 that occurs with refraction of the sound beam in passing through the water body either toward or away from the surface can be determined by measurement of thev change in velocity of sound in the water body and that angle 0 varies with the sound velocity. This can be justified by Snells law of refraction lconsidered in connection with Figure 2. In the diagram a sound beam A is considered passing downward through a horizontal interface LL of two layers of a water body and refracted at point P. The circle is of unit radius for convenience. NN is normal to LL. Lines ab and ab' are parallel to NN and the lines bq and qb are parallel to LL. Also v1 equals the sound Velocity above LL and v2 equals the sound velocity below LL. I is the angle of incidence; I is the angle `of refraction. 0 is the observed angle of depression; 0' .is 'the retracted angle of depression. From Snells law of refraction:

R (yards) Thus angle 0 varies with the sound velocity. From the equation D(feet) 1 R(yards)= 3 X tan 0 it is seen that horizontal range R. varies with angle e and therefore horizontal range R varies with sound velocity; measurement of sound velocity is therefore a factor in computing horizontal range. Thus when a sound beam passes through layers of water having different soundtransmitting characteristics, which cause refraction of the beam, it is possible by making observations of the speed of sound in the different layers to include proper refraction corrections in computing the horizontal range.

Applicant has found that instead of using sound velocity as the water characteristic to be observed there are other characteristics that are observable and affect horizontal range determination. One such characteristic is the thermal structure of the water; which often is found in substantially horizontal layers; the water may have a negative temperature gradient (decrease in temperature with increase in depth below the surface) or there may exist a positive temperature gradient (increase in temperature with increase in depth below the surface) or there may exist a mixed layer of water above either a negative or positive gradient layer; or there may exist isothermal conditions (uniform temperature with change in depth below the surface). Another characteristic is the surface temperature of the water. Another characteristic is the salinity and density of the water. Data obtained by observation of these characteristics for a particular body of water can be used in determining the refraction of the sound beam and computing the horizontal range R. This method of computation has the disadvantage of requiring observations of several different characteristics and inclusion of the several different observations in the computation.

Computation of the horizontal range has heretofore been a cumbersome process involving substitution of observed values in a formula and necessitating the use of numerous graphs representing the functional relationship between variation of range with variation in characteristics of the water body.

Applicant has overcome the difficulties of computation by providing a slide rule of simple construction for computing the value of horizontal range. A rst xed scale is graduated in terms of depth (of an observer). A second fixed scale is graduated in terms of range (of target). A sliding scale is graduated in terms of angle of elevation (angle and registers with the rst fixed scale. The lower edge of the slide is provided with an index mark. The face of the slide is inscribed with curves representing change in sound velocity with change in angle 0 (and hence change in range). The cursor is graduated across the face of the slide in terms of change in velocity. AV.

An object of the invention is to provide a device for computing from observed data the range of a target relative to an observer.

Another object is to provide a slide rule for computing the range of a marine target relative to a marine observer from observed sound echo data.

Another object is to provide a slide rule for computing the range of a marine target relative to a marine observer from sound echo data in which the computation takes into account refraction of the sound beam.

Another object is to provide a slide rule for computing range of a target relative to an observer from sound echo data in which the slide rule is arranged to take into account refraction of the sound beam between layers of water having different sound-transmission characteristics.

Another object is to provide a slide rule for computing range of a target relative to an observer from sound echo data in which the slide rule is arranged to take into account refraction of the sound beam between layers of water having different sound-velocity characteristics.

Another object is to provide a slide rule for computing the range of a marine target relative to a marine observer from sound echo data in which a first fixed scale is graduated in terms of depth (of an observer); a second fixed scale is graduated in terms of range (of target); a sliding scale is graduated in terms of angle of elevation (angle 0) and registers with the first fixed scale; the lower edge of the slide is provided with an index mark; the face of the slide is inscribed with curves representing change in sound velocity with change in angle 0 (and hence change in range); and a cursor is graduated across the face of the slide in terms of change in velocity, AV.

Further objects and advantages of this invention as well as its construction, arrangement and operation will be apparent from the following description and claims in connection with the accompanying drawing in which the gure is a plan view of a preferred embodiment of the invention.

In the figure is shown a body I having spaced rails 2 and 3, which define a channel 4 therebetween. A slide 5 is mounted in channel 4 for sliding movement between rails 2 and 3. Mounted transversely across slide 5 and across rails 2 and 3 is a cursor 6 provided with end guides `I and 8 for engaging the outer surfaces of rails 2 and 3 to guide cursor 6 for sliding movement along rails 2 and 3. The surfaces of rails 2 and 3 and of slide 5 are formed of opaque material capable of being inscribed with markings. The portion of cursor 5 extending across rails 2 and 3 and slide 5 is transparent and capable of being inscribed with markings.

Rail 2 is inscribed with a scale 9 graduated to represent log depth in terms of linear feet. Scale 9 is provided with a first series Il of identifying numbers from 10 to 100 and with a second series I2 of identifying numbers from 100 to 1,000. The dual set of numbers is used in order to provide a slide rule of minimum length.

Rail 3 is inscribed with a scale I3 graduated to represent log range in terms of linear yards. Scale I3 is provided with a first series I4 of identifying numbers from to 1,000 and a second series I5 of identifying numbers from 1,000 to 10,000. Series I 4 of scale I3 is for use with series II of scale 9 and series I5 of scale I3 is for use with series I2 of scale 9. Scales 9 and I3 are of equal length and are aligned transversely of body I.

Slide 5 adjacent rail 2 is inscribed with a scale I6 graduated to represent log tan inclination angle 0 and is provided with a series I1 of identifying numbers from 2.5 to 26. From the graduations of scale I6 as points of origin, there are plotted a series of curves I8 and a second superimposed series of curves I9. Curves I8 slope downwardly and to the left from the points of origin and represent log tan 0 plotted as abscissa. points against velocity difference plotted as ordinate points. Velocity difference increases in a downward direction and log tan 0 increases toward the right. Curves I8 represent a positive gradient condition in which increases in velocity The vinvention described herein maybe manufactured and used by or for the Government of the United States of America for governmental purposes without the payment of any royalties thereon or therefor.

What is claimed is:

1. A slide rule comprising a body member and aslide member, a iirst scale on said body member and a second scale on said slide member adapted to register with the iirst scale, graduations'on therst scale representing log depth of an observer, 'graduations on the second scale representing log' tangent of the angle of inclination of a target relative tothe observer, a third scale on'one of said members; graduations o'n the third scale representing log range 'of the target, an index on the other of said members adapted for registration with the third scale, curves inscribed on the slide representing change in log range ofthe target withchange in velocity of an echo beam between the observer and target, a cursor, and graduations on the cursor representing change in velocity and adapted for registration with said curves, said curves having their respecitive points of origin at respective ones of said graduations and said cursor being slidable over said body member and said slide member.

2. A slide rule comprising a body member and a slide member, a iirst scale on said body member and a second scale on said slide member adapted to register with the iirst scale, graduations on the nrst scale representing log depth of an observer, graduations on the second scale representing log tangent of the anglev of inclination of a target relative to the observer, a third scale on one of said members, graduations on the third scale representing lo'g range of the target, an index on the other of said members adapted for registration with the third scale, a first set of curves inscribed on the slide representing change in log tan average angle of inclination' plotted against increasing changes in velocity of a refracted echo beam between the observer and target, and a second set of curvesv superimposed on the rst set of curves with common points of origin and representing changes vin log tan average angle of inclination plotted against decreasing change' in velocity of a refracted echo beam between the observer and target, said curves having their respective points of origin at respective ones of said graduations.

3. A slide'rule comprising a body member and.

a slide member, a i'lrst scale on said body member and a second scale on said slide member adapted to register with the rst scale, graduations on the first scale representing log depth of an o bserver, graduations on the second scale representing log tangent of the angle of inclination of a target relative to the observer, a third scale on one of said members, graduations on the third scale representing log range of the target, an index on the other of said members adapted-for registration With the third scale, a iirst set'pf curves inscribed on the slide representing change in log tan average angle of inclination plotted against increasing change in velocity of a -refracted echo beam between the observeruand target, and a second set of curves superimposed on the first set of curves with common points of origin and representing changes in` log tanv average angle of inclination plotted against d e-` creasing change in velocity of a refracted echo beam, a cursor, and graduations on the cursor representing change in velocity and adapted-for registration with said curves, said curves having their respective points of origin at respective'l ones of said graduations and said cursor being slidable over said body member and said slide member.

DONALDL. COLE.

assumptions @iran The following references are of record in the file ci this patent:

UNITED STATES PATENTS Number Name Date 1,568,475 Schwanda .I an. 5, 1926 2,219,429 Osterberg Oct. 29, 1940 OTHER REFERENCES Pages 19-29 of spcial suce mies,"v by J. N.

Arnold, published as Engineering Bulletin, Ex'ten'- Darsten, published by Prentice-Hall, Inc., New" York in 1923.

difference downwardly from the surface of the water body is accompanied by decrease in log tan 6. Curves I9 slope downwardly and to the right from the points of origin. Curves I9 represent a negative gradient condition.

A pair of index arrows 2I and 22 are provided at the edge of slide 5 adjacent scale I3. Arrows 2 I and 22 are spaced a distance equal to the length of scales 9 and I3. Arrows 2I and 22 are positioned relative to scale I6 to represent a constant of log 3.

Cursor 6 is inscribed with a hairline 23 provided with graduations 24 representing increase in velocity difference from Zero value at scale I6 to maximum value adjacent scale I3.

Curves I8 and I9 are preferably constructed from data that are mathematically computed by use of Snells law of refraction. If desired, however, the curves can be constructed directly from data obtained in actual sound echo operations f or by use of empirical formulas derived from such data.

There is provided for curves I8 and I9 a limiting boundary 2o since it is found in operation that curves extending beyond the boundary are impracticable. Curves in the area beyond boundary have a relatively large cha-nge in ordinate for a relatively small change in abscissa and thus provide inaccurate results in use of the slide rule. Interpolation of values is made between the various curves I8 and the various curves I9 in use of the slide rule.

Instead of curves I8 and I9, which represent change in log tan 6 with change in velocity, other curves may be inscribed upon slide 5. For example, the curves can be constructed to represent change in log cot 6 with change in velocity. Or curves can be constructed which, instead of being based upon change in sound velocity, are based upon changes in characteristics of the water body such as change in thermal structure, surface temperature or salinity. Such characteristics can be observed directly in actual sound echo operations. If such alternate curves are used, scales 9 and I3 are suitably modified so that the slide rule will be operable for computing the desired quantity.

The slide rule is constructed to solve the basic equation stated hereinbefore:

R (yards),

log R(yards) :log D(feet)-log tan 6-log 3 The construction of the slide rule is such that the above equation can be solved without the use of curves I3 and I S for the special condition of constant velocity of sound in the water body at all observed depths (temperature of the water body). For example, under this condition and in the case of a submerged observing submarine and a surface target vessel, this is accomplished for any particular set of observed data by selecting the appropriate graduation on scale 9 representing the observers depth, bringing into registration therewith the appropriate graduation on scale IE representing the observed inclination angle 6 and reading the range (answer) on scale I3 Where indicated by arrow 2| or arrow 22. This procedure subtracts from log D (on scale 9) the logr tan 6 (on scale I 6) and also the constant log 3 (because of the position of arrows 2I and 22 relative to scale I 8).

Under more usual conditions of operation illustrated in Figure 3, a sound beam in passing upward from A through Water layers having different sound velocity characteristics follows the dotted line path which is not a straight line. Under these conditions tan 6 changes with velocity change and in computing R by the above equation it is necessary to modify the value of log tan 6 in order to compute the correct value of R. Such correction is introduced in operation of the slide rule by the use of curves I8 and I9 which represent log tan 6 plotted as abscissa points against velocity diiTerence plotted as ordinate points. The abscissa or change in log tan 6 are components of the curves parallel to scale I3 and are thus the components used for correcting the computed range in scale I3. The velocity difference is the change in velocity of a sound beam from the entrance point to the exit point of any particular layer of the water body and the angle 6 is the average angle for such layer calculated by adding the entrance and exit angles and dividing by 2. Curves I8 represent change in log tan 6 for positive change or increase in velocity; curves IS represent change in log tan 6 for negative change or decrease in velocity. As seen from the equation above, an increase in log tan 6 (with decrease in velocity) results in a decrease in actual range compared with apparent range; conversely a decrease in log tan 6 (with increase in velocity) results in an increase in actual range compared with apparent range.

To illustrate use of the slide rule in solving for range of a surface target observed from a, submerged submarine the case is considered of a submarine at a keel depth of 300 feet and having a hydrophone located 10 feet above the keel to provide a hydrophone depth of 290 feet. Observations indicate an increase in the velocity J of sound of feet per second from the water surface to the indicated depth. Sound echo observations indicate an angle of elevation, 6, of 12. Computation of horizontal range is accomplished as follows (see the figure):

Cursor 6 is adjusted until hairline 23 thereof is in registration with the graduation representing a depth of 290 feet on scale 9. Slide 5 is then adjusted until curve I8 (for positive or increasing velocity) from the graduation representing an origin angle 6 of 12 on scale I6 intersects the cursor graduation representing velocity change of 65 feet per second at hairline 23. Arrow 22 indicates a range of 558 feet on scale I3 as the answer. This solution is for a single layer of water. If, however, there are other overlying layers of water, the process is repeated for each layer. In such case the new origin angle 6 is determined by following a curve I9 from the above intersection back to scale I6 where an interpolated value (in the example) of '7 45 is indicated. This procedure is justified since 12 and 7 45 represent the inclination angles made by the sound beam at the boundaries of the water layer and their average value is represented at their point of intersection.

In the stated problem a positive or increasing value of velocity change was involved and curves I8 were used in solving for range. If a negative or decreasing value of velocity change is involved in a problem, curves I9 are used in solving for range.

It is to be understood that various modifications and changes may be made in this invention without departing from the spirit and scope thereof as set forth in the appended claims. 

